Question: Solve for $x$ and $y$ using elimination. ${4x+y = 27}$ ${-5x-y = -32}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {4x+y = 27}\thinspace$ to find $y$ ${4}{(5)}{ + y = 27}$ $20+y = 27$ $20{-20} + y = 27{-20}$ ${y = 7}$ You can also plug ${x = 5}$ into $\thinspace {-5x-y = -32}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ - y = -32}$ ${y = 7}$